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Arithmetic system using minimal signed-digit number representation for residue exponential operations with long word length

Research Project

Project/Area Number 23500057
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Computer system/Network
Research InstitutionGunma University

Principal Investigator

WEI Shugang  群馬大学, 大学院理工学府, 教授 (10251125)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords最小SD数表現 / VLSIシステム / 算術演算システム / 剰余演算 / 算術演算 / 剰余演算システム / VLSIアルゴリズム / 剰余演算,ギリシャ / 剰余数系の変換,台湾 / 剰余乗算
Outline of Final Research Achievements

New algorithms using minimal signed-digit (SD) number representation for the residue exponential operations with long word length were presented. A binary recoding method for the SD number is used for implementing the residue additions. By applying the recoding and the minimal signed-digit number representation, the residue addition circuit performance was modified. The proposed residue arithmetic circuits can be applied for the implementation of the RSA encryption with very long word length. To reduce the complexity of the residue operations, an efficient algorithm has been also proposed to obtain the minimal signed-digit number representations.
The design and simulation results show that high-speed exponential operations can be implemented by the proposed method.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (19 results)

All 2014 2013 2012 2011

All Journal Article (19 results) (of which Peer Reviewed: 14 results,  Open Access: 2 results)

  • [Journal Article] Residue Checker Using Signed-Digit Adder Tree for Error Detection of Arithmetic Circuits2014

    • Author(s)
      S.Wei
    • Journal Title

      IEEE Proceedings of TENCON2014.

      Volume: 1 Pages: 371-374

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Conversions between RNS and Mixed-Radix Numbers Using Signed-Digit Arithmetic2014

    • Author(s)
      S.Wei
    • Journal Title

      Proceedings of 2014 IEEE International Symposium on Integrated Circuits

      Volume: 1 Pages: 600-603

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 剰余SD数演算回路を用いた算術演算誤り検出2014

    • Author(s)
      根間裕智、田中勇樹、茂木和広、魏書剛
    • Journal Title

      信学技報VLD2014

      Volume: 136 Pages: 151-156

    • NAID

      110009868159

    • Related Report
      2014 Annual Research Report
  • [Journal Article] Residue-Weighted Number Conversion for Moduli Set {2n-1, 2n+1, 22n+1, 2n} Using Signed-Digit Number2013

    • Author(s)
      C. Jiang and S. Wei
    • Journal Title

      Journal of Circuits, Systems, and Computers

      Volume: 22 Issue: 01 Pages: 1-17

    • DOI

      10.1142/s0218126612500703

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] New Binary Modular Adder Tree Structure for Arithmetic of Error Checker of Arithmetic2013

    • Author(s)
      M. Zhang and S. Wei
    • Journal Title

      Journal of Communication and Computer

      Volume: 10 Pages: 295-300

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] High-Speed Modular multipliers Based on a New Binary Signed-Digit Adder Tree Structure2013

    • Author(s)
      M. Zhang and S. Wei
    • Journal Title

      Journal of Circuits, Systems, and Computers

      Volume: 22 Issue: 06 Pages: 1-18

    • DOI

      10.1142/s0218126613500436

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Residue-Weighted Number Conversion Using Signed-Digit Number for Moduli Set {22n-1, 22n+1+1, 2n},2013

    • Author(s)
      C. Jiang and S. Wei
    • Journal Title

      Analog Integrated Circuits and Signal Processing

      Volume: 77 Pages: 105-112

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] An Advanced Implementation of Canonical Signed-Digit Recoding Circuit2013

    • Author(s)
      Y. Tanaka, and S. Wei
    • Journal Title

      Journal of Communication and Computer

      Volume: 11 Pages: 1396-1402

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] SD数演算を用いたRSA暗号処理回路の設計の性能評価2013

    • Author(s)
      浅岡隼一、田中勇喜、議書剛
    • Journal Title

      信学技報

      Volume: 115 Pages: 45-50

    • Related Report
      2012 Research-status Report
  • [Journal Article] Residue-Weighted Number Conversion for Moduli Set {22n-1, 22n+1+1, 2n} Using Signed-Digit Number2012

    • Author(s)
      C. Jiang and S. Wei
    • Journal Title

      Proceedings of the 10th Annual IEEE Northeast Workshop on Circuits and Systems

      Volume: 1 Pages: 9-12

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] 剰余SD数の非零桁数を削減する変換アルゴリズム2012

    • Author(s)
      田中勇樹、魏書剛
    • Journal Title

      第25回回路とシステムワークショップ論文集

      Volume: 1 Pages: 156-159

    • NAID

      40019433840

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sequential Modular Multipliers Using Residue Signed-Digit Additions2012

    • Author(s)
      S. Wei
    • Journal Title

      Journal of Communication and Computer

      Volume: 8 Pages: 872-878

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Residue Signed-Digit Arithmetic and the Conversion between Residue and Binary Numbers for a Four-Moduli Set2012

    • Author(s)
      S. Wei and C. Jiang
    • Journal Title

      Proceedings of 11th International Symposium on Distributed Computing and Applications to Business, Engineering and Science

      Volume: 1 Pages: 436-440

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] An RSA encryption Implementation Method Using Signed-Digit Arithmetic Circuits2012

    • Author(s)
      S. Wei
    • Journal Title

      IEEE Proceedings of 5th International Conference on Biomedical Engineering and Informatics

      Volume: 1 Pages: 1337-1341

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] SD数の2値符号化による算術演算回路の最適化設計と性能評価2012

    • Author(s)
      小林拓矢、茂木和弘、魏書剛
    • Journal Title

      信学技報

      Volume: 115 Pages: 39-44

    • Related Report
      2012 Research-status Report
  • [Journal Article] 2分木構造の剰余SD数演算を用いた算術演算エラー検出回路2012

    • Author(s)
      劉茜、茂木和弘、魏 書剛
    • Journal Title

      電子情報通信学会研究報告

      Volume: VLD2011-110 Pages: 117-121

    • NAID

      10031098325

    • Related Report
      2011 Research-status Report
  • [Journal Article] SD数演算を剰余数系―重み数系変換アルゴリズム2012

    • Author(s)
      新井聖哉、田中勇樹、魏 書剛
    • Journal Title

      電子情報通信学会研究報告

      Volume: VLD2011-110 Pages: 111-116

    • Related Report
      2011 Research-status Report
  • [Journal Article] A Sequential Modular Multiplication Algorithm Using Signed-Digit Additions2011

    • Author(s)
      S. Wei(魏 書剛)
    • Journal Title

      IEEE Proceedings of TENCON2011

      Volume: 1 Pages: 370-374

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Efficient Residue Checker Using New Binary Modular Adder Tree Structure for Arithmetic of Error Detection2011

    • Author(s)
      M. Zhang and S. Wei
    • Journal Title

      Proceedings of Eighth International Conference on Fuzzy Systems and Knowledge Discovery

      Volume: 3 Pages: 2481-2485

    • Related Report
      2011 Research-status Report
    • Peer Reviewed

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Published: 2011-08-05   Modified: 2019-07-29  

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